Question: Solve for $x$ and $y$ using elimination. ${-x+6y = 27}$ ${x+5y = 39}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $11y = 66$ $\dfrac{11y}{{11}} = \dfrac{66}{{11}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-x+6y = 27}\thinspace$ to find $x$ ${-x + 6}{(6)}{= 27}$ $-x+36 = 27$ $-x+36{-36} = 27{-36}$ $-x = -9$ $\dfrac{-x}{{-1}} = \dfrac{-9}{{-1}}$ ${x = 9}$ You can also plug ${y = 6}$ into $\thinspace {x+5y = 39}\thinspace$ and get the same answer for $x$ : ${x + 5}{(6)}{= 39}$ ${x = 9}$